[论文解读] A Compression-Complexity Measure of Integrated Information

Mohit Virmani, Nithin Nagaraj|arXiv (Cornell University)|Aug 23, 2016

Fractal and DNA sequence analysis参考文献 3被引用 4

一句话总结

本文提出了ΦC，一种新型的整合信息压缩-复杂度度量方法，通过计算效率高、状态无关且适用于真实神经数据，克服了整合信息理论（IIT）的关键局限。该方法利用无损压缩（ETC和LZ）量化动态复杂性，在不同网络中展现出与Φ一致的强层级结构，并建立了整合、分化与熵之间的稳健关联。

ABSTRACT

Quantifying integrated information is a leading approach towards building a fundamental theory of consciousness. Integrated Information Theory (IIT) has gained attention in this regard due to its theoretically strong framework. However, it faces some limitations such as current state dependence, computationally expensive and inability to be applied to real brain data. On the other hand, Perturbational Complexity Index (PCI) is a clinical measure for distinguishing different levels of consciousness. Though PCI claims to capture the functional differentiation and integration in brain networks (similar to IIT), its link to integrated information theories is rather weak. Inspired by these two approaches, we propose a new measure - $Φ^C$ using a novel compression-complexity perspective that serves as a bridge between the two, for the first time. $Φ^C$ is founded on the principles of lossless data compression based complexity measures which characterize the dynamical complexity of brain networks. $Φ^{C}$ exhibits following salient innovations: (i) mathematically well bounded, (ii) negligible current state dependence unlike $Φ$, (iii) integrated information measured as compression-complexity rather than as an infotheoretic quantity, and (iv) faster to compute since number of atomic bipartitions scales linearly with the number of nodes of the network, thus avoiding combinatorial explosion. Our computer simulations show that $Φ^C$ has similar hierarchy to $$ for several multiple-node networks and it demonstrates a rich interplay between differentiation, integration and entropy of the nodes of a network. $Φ^C$ is a promising heuristic measure to characterize the quantity of integrated information (and hence a measure of quantity of consciousness) in larger networks like human brain and provides an opportunity to test the predictions of brain complexity on real neural data.

研究动机与目标

• 解决大规模网络中整合信息（Φ）计算不可行性和当前状态依赖性问题。
• 弥合整合信息理论（IIT）与临床使用的扰动复杂性指数（PCI）之间的理论差距。
• 基于数据压缩原理，开发一种可扩展、稳健且具有神经生理学适用性的整合信息度量方法。
• 使基于复杂系统真实神经时间序列数据的意识理论测试成为可能。

提出的方法

• 提出基于努力压缩（ETC）和伦佩尔-利瓦尔德（LZ）复杂度的ΦC压缩-复杂度度量方法，用于量化动态复杂性。
• 对单个节点施加扰动，并计算其余节点的差分压缩-复杂度响应分布（dCCRD）。
• 对所有原子二分划（如A–BC、B–AC、C–AB）的dCCRD值进行聚合，以计算聚合差分压缩-复杂度度量。
• 将最终度量定义为所有可能二分划中所有聚合dCCRD值的最大值，即ETCΦC。
• 使用线性回归模型将整合信息建模为节点熵和网络规模的函数，拟合系数以从熵分量预测ΦC。
• 在包含XOR、AND和OR逻辑门的合成网络以及具有放电动力学的Hindmarsh-Rose神经元模型上验证该方法。

实验结果

研究问题

• RQ1 压缩-复杂度度量能否在小型网络中复现Φ的层级结构？
• RQ2 ΦC在计算成本和对网络状态的敏感性方面与Φ相比如何？
• RQ3 在合成逻辑网络中，ΦC与熵和网络规模的相关性有多大？
• RQ4 ΦC能否在Hindmarsh-Rose等生物真实神经元模型的时间序列上可靠计算？
• RQ5 ΦC在复杂网络中是否展现出整合、分化与熵之间的有意义相互作用？

主要发现

• ΦC在所有3节点逻辑网络中均表现出与<Φ>一致的层级结构，回归分析中预测值（Ŷ）与实际<Φ>值高度吻合。
• 使用nhighHhigh和nlowHlow作为预测变量的线性回归模型拟合良好，其中ˆxhigh = 1.11，ˆxlow = 0.1408，表明具有强大的解释力。
• ΦC计算效率高，二分划复杂度随节点数线性增长，避免了Φ的组合爆炸问题。
• 对于Hindmarsh-Rose模型，使用I = 3.310（规则放电）和I = 3.28（混沌放电）的放电序列计算熵和压缩复杂度。
• 在3节点示例中，所有二分划的最大ETCΦC值为0.548，即所有聚合dCCRD值的最大值。
• ΦC表现出可忽略的当前状态依赖性，与Φ不同，且数学上边界良好，适用于实际应用。